Black-Scholes Assumptions

Assumptions of the Black-Scholes Option Pricing Model

  • No riskless arbitrage opportunity exists.
  • There are zero transaction costs.
  • There are no restrictions to short selling of the underlying security.
  • You can buy or sell any quantity of the underlying security, even a fraction (e.g. 0.1843 shares).
  • You can borrow or lend cash, in any quantity, at a constant risk-free interest rate (this risk-free interest rate is one of the parameters entering the calculation of option prices).
  • Future direction of the price of the underlying security can’t be predicted. The price makes a “random walk”. This also means that:
    • Returns are normally distributed.
    • Prices are log-normally distributed.